High-bandwidth technologies which are prevalent nowadays use the existing copper wire infrastructure intended for plain old telephones (POTS) communication. One such technology is Digital Subscriber Line (DSL) which comes in multiple variations such as ADSL, HDSL, IDSL, SDSL, RADSL and VDSL collectively known as xDSL. Asymmetric digital subscriber line (ADSL) allows users a higher data rate downstream (i.e. to the customer) than upstream (i.e. the service provider).
These high-bandwidth systems use single-carrier modulation as well as multi-carrier modulation schemes, such as Carrier-less Amplitude and Phase modulation (CAP) and Discrete Multi-tone (DMT) for wired media and Orthogonal Frequency Division Multiplexing (OFDM) for wireless communication. One advantage of such schemes is that they are suited for high-bandwidth application of 2 Mbps or higher upstream (subscriber to provider) and up to 8 Mbps downstream (provider to subscriber). Quadrature Amplitude Modulation (QAM) utilizes a sine and cosine wave with the same frequency component to convey the information. The x and y components of the point to which the bits are mapped specify the amplitude of the sine and cosine waves and, because of the orthogonality between the waves, the data can be sent over the channel simultaneously. The amplitude (including sign and magnitude) of each wave conveys the information (bits) being sent. QAM modulation has been used in voice-band modem specifications, including the V.34.
CAP is similar to QAM. For transmission in each direction CAP systems use two carriers of identical frequency above the 4 KHz voice band, one shifted 90 degrees relative to the other. CAP also uses a constellation to encode bits at the transmitter and decode bits at the receiver. The x and y results from the encoding process are then used to excite a digital filter.
DMT modulation, sometimes called orthogonal frequency division multiplexing (OFDM), builds on some of the ideas of QAM but, unlike QAM, it uses more than one constellation encoder where each encoder receives a set of bits that are encoded and outputs the amplitude of the sine and cosine waves. However, a different sine and cosine frequency is used for each constellation encoder. The outputs from these different encoders are summed together and sent over a single channel for each direction of transmission. DMT systems divide the spectrum above the 4-KHz voice frequency band into 256 narrow channels called bins (sometimes referred to as tones, DMT tones or sub-channels). These bins are 4.3125 KHz wide. The waveforms in each bin are completely separable from one another. One key to separability is that the sine and cosine frequencies used in each bin should be multiples of a common frequency known as the fundamental frequency and in addition the symbol period τ, must be the inverse of the common frequency. Another of way of producing a DMT symbol, other than mapping the output of the constellation encoder into a sine and cosine amplitude, is that the output can be mapped into a complex number in a vector. The value from the cosine axis, or X will represent the real part and the value from the sine axis, or Y will represent the imaginary part. If the outputs of all the constellation encoders are ordered in the vector, then each vector point represents one of the DMT bins and, if N bins existed in the DMT system, the complex vector would have N entries. A suffix containing the complex conjugates of the vector's original entries can be added to the vector such that the new vector has complex conjugate symmetry. An inverse Fourier transform (IFFT) on those N frequency bins is then used to convert the data from frequency domain to a time domain signal.
From a circuit standpoint, and in relation to discrete multi-tone modulation, the prior art shown in FIG. 1, is a transmitter side of a DMT transceiver. The transmitter accepts serial data which is then converted from serial to parallel form and to provide two hundred fifty-six signals n0-n255 via a serial to parallel converter 10 (P/S). The sequences are then passed on to a symbol-mapper 20 where each bit is assigned or mapped into one of N-complex (QAM) multi-level sub-symbols. The two hundred fifty-six symbols are complex-valued and are fed into an IFFT 30 which provides five hundred and twelve output real signals by taking the complex conjugates of the two hundred fifty six samples. The parallel outputs of the IFFT are applied to a cyclic prefix 40 which helps to make a channel circular so that equalization can occur more easily in the frequency domain. The output of the cyclic prefix block is then applied to a parallel to serial converter 50 to provide a serial output signal which is upsampled and interpolated by a digital filter 60. The output is processed by a digital-to-analog converter (DAC) 70 which converts the discrete time signal into a continuous time signal.
Spurious high amplitude peaks in the composite time signal occur when the signals from the different tones add constructively. Compared to the average signal power, the instantaneous power of these peaks are high, and consequently, so is the peak-to-average power ratio (PAR). These large peaks require a large dynamic range of the analog-to-digital converter (ADC) and analog front end (AFE) which result in inefficient amplifiers with excessive power dissipation and expensive transceivers. To overcome the drawbacks of the high PAR, many solutions and techniques have been proposed, one of which is, tone reservation method in which a pre-selected number of tones are set aside for PAR reduction. The information transmitted in these tones are used to subtract from the signal envelope, thus reducing the PAR, but at a cost of increased complexity at the transmitter.
Another method depends upon applying a combination of saturating non-linearity (clipping) at the transmitter and having the knowledge of the saturating characteristics at the receiver to iteratively decode the data vector without distortion by performing a number of tedious and costly fast FFT and IFFT computations.
Yet another method, known as selective mapping, involves generating a large set of data vectors all representing the same information in which the data vector with lowest PAR is selected. However, potential problems may arise with decoding the signal in the presence of noise where errors in the reverse mapping may result in the data of whole symbols being lost. Other drawbacks also exist.